If You Know Their Rules ...
You Can Play Their Games

`If the appraisal does not match the highest figure that you received from the three used-car operations, tell the salesperson that you have a higher offer and that if the used-car department can't do better-don't tell them how much better-you may have to look elsewhere. At this point, the salesperson may suggest that you write up the deal. Indicate that you'll be prepared to deal when the appraisal is competitive with those you've already received.

Appraisal, Not Allowance
If the salesperson comes back and talks about how much they are prepared to "allow" you on your trade, be pleasant and remind the salesperson that you did not ask for an allowance, but an appraisal. Your objective here is to eliminate-or at least minimize-dealership injected confusion by keeping each element of the transaction as a separate issue.

When a dealership offers you more for your trade-in than the wholesale price, it may be that you have a car that is so much in demand they are confident they can sell it immediately for considerably more than they're paying. Or the salesperson may perceive you as someone who is more intent on getting a good price for your trade than getting a discount off the new car (a "difference" buyer). All the dealership is doing is moving the discount off the new car onto the trade-in price of your current car.

Negotiating the, Deal

Assuming that the dealership raises their offer to an acceptable amount on your trade-in, you can turn your attention to the new car. Tell the salesperson, in a nice way, that you'd like to see if you can make a deal and that you hope the two of you can come to some agreement within the next half hour because you have an appointment at another dealership. (Salespeople like to use a time-pressure ploy on their customers. This is one way to turn it back on them.)